Oligopoly

Chapter 17 Oligopoly 17.1 Introduction In this chapter we continue our study of market structure by looking at oligopoly or an industry with few producers. We will continue to assume that firms in the industry wish to maximize profits. This would lead firms to collude. That is, firms would like to agree to restrict output to monopoly levels and then split the profits. This could give all the firms in the industry higher profits that they would obtain if they competed. The interesting question, then, is to determine why firms do not collude and if they do not collude, how do they compete. Therefore, we will see that industry equilibrium is characterized by the proper balance between cooperation and competition.   In order to study oligopolistic market structure, we first need to invest a little bit in tools. The key characteristic of oligopolistic industries is the presence of strategic interactions among firms. This arises from the fact that with few firms in the industry, the elasticity of market demand depends on the output of each firm. Therefore, one firm has a direct impact on the price that the other firms in the industry can charge. In monopoly and perfect competition this ingredient was missing. Therefore, we will introduce the concept of a Nash Equilibrium to study the pure, non-cooperative outcome. We will study two ways in which firms compete. We will look at Cournot competition which means that firms compete in quantities and at Bertrand competition which means firms compete in prices. We will also see that as the number of firms in the industry increases   Continuation from the previous image: -equivalently, as market share falls, the importance of strategic interactions diminishes and we approximate the competitive solution. Similarly, as the number of firms approaches 1, we will see that we also approach the monopoly solution (take with a grain of salt since threat also matters). 17.2 The Perfectly Competitive Benchmark Let us compute the perfectly competitive benchmark solution to the the oligopoly equilibrium first. 17.2.1 Firms Suppose that there are fixed number (few) of firms in the industry - two firms, in this case - and that they each have one plant. We assume that marginal costs are constant. Therefore, each firms cost function is linear in output and equal to: [C(y_{i})=c_{i}y_{i},] where (y_{i}.) for (i=1,2,) denotes each firm's output. Each firm's profit maximization problem is given by: [max_{y_{i}} py_{i}-C(y_{i}).] Suppose that the firms believe that they can not influence market price through their quantity choice and that collusion is impossible or extremely costly. Then, the firms operate in a perfectly competitive market and the first order conditions tell us that each firm will produce where price equals marginal cost: [[y_{i}]:p=c_{i},] so each firm supplies output inelastically. Each firms profit is exactly equal to 0. 17.2.2 Equilibrium Let us suppose for simplicity that firms are identical and the market demand function is given by the following linear demand curve: [Y(p)=\frac{a-p}{b}.] 17.4.2 The Cartel Game Suppose we set up the payoff matrix for the cartel game we are analyzing in this chapter. The payoff matrix in general form is given below. The rows of the matrix contain Firm 1's possible actions while the columns contain Firm 2's strategies. Both firms can either collude or renege. Notice that profit levels are jointly determined by both firms' actions since the actual profit level each firm receives from depends on whether it colludes or reneges and also on whether its competitor colludes or reneges (since πi is a function of y1 and y2). This is the nature of the strategic interaction. The payoff matrix below then, contains the general statement of the game. \[\begin{matrix} & C & R \\ C & \pi_{1}(y_{1}^{C},y_{2}^{C}), \pi_{2}(y_{1}^{C},y_{2}^{C}) & \pi_{1}(y_{1}^{C},y_{2}^{R}), \pi_{2}(y_{1}^{C},y_{2}^{R}) \\ R & \pi_{1}(y_{1}^{R},y_{2}^{C}), \pi_{2}(y_{1}^{R},y_{2}^{C}) & \pi_{1}(y_{1}^{R},y_{2}^{R}), \pi_{2}(y_{1}^{R},y_{2}^{R}) \\ \end{matrix}\] Let us, however, replace the payoffs with the actual payoffs from the cartel with symmetric cost functions and linear demand. We obtain: \[\begin{matrix} & C & R \\ C & \frac{(a-c)^{2}}{4b}, \frac{(a-c)^{2}}{4b} & \frac{(a-c)^{2}}{8b}, \frac{9(a-c)^{2}}{16b} \\ R & \frac{9(a-c)^{2}}{16b}, \frac{(a-c)^{2}}{8b} & \frac{(a-c)^{2}}{9b}, \frac{(a-c)^{2}}{9b} \\ \end{matrix}\] Notice that if firm 1 chooses to collude, then firm 2 finds it optimal to renege on the contract since \[\frac{9(a-c)^{2}}{16b} > \frac{(a-c)^{2}}{8b}.\] Similarly, if firm 1 chooses to renege, firm 2 should also renege since \[\frac{(a-c)^{2}}{9b} > \frac{3(a-c)^{2}}{32b}.\] The analysis is perfectly symmetric. In the absence of a mechanism that controls cheating (a self-enforcing agreement) both firms find it in their self-interest to renege on the contract. The Nash equilibrium is, then, for both firms to renege on the contract even though collusion gives them higher profits!